We present our results in section . First we note that the two limits \(\beta /\alpha \rightarrow 1\)  and \(\beta /\alpha \rightarrow \infty \) , or
equivalently, \(\beta /\alpha \rightarrow 0\)  correspond to the directed percolation [1]} and the directed polymer problems
respectively [2]}. This
points us in the direction of there being a critical point in the problem in spite of the conclusion drawn for the capillary
fiber bundle model in section . Indeed, this is what we find: We find that \(\langle q\rangle -\langle q_c\rangle \sim (\nabla p-\nabla p_c)^\mu \)  where \(\mu \)  depends on the ratio \(\beta /\alpha \)  for the same type of treshold distribution that gave
a power law dependence in the capillary fiber bundle model studied in section . We define and measure a correlation length
\(L_{\max }\sim (\nabla p-\nabla p_c)^{-\nu }\) . The correlation length exponent \(\nu \)  also depends on the ratio \(\beta /\alpha \) . In the
limit \(\beta /\alpha \rightarrow 1\) , the longitudinal directed percolation correlation length exponent \(\nu _\parallel =1.733847(6)\)  [3]}
is expected and our numerical results are consistent with this. In the directed polymer
limit \(\beta /\alpha \rightarrow \infty \) , however, the corresponding correlation length exponent is not the usual one, \(\nu _\parallel =3/2\) 
[4]}, but rather one that describes a correlated directed percolation problem.
